I am posting this in behalf of a friend of mine from a distant world. Here is his message properly translated to English:
Hi, Sol3αlings1. My name is $ѬӚᕕƨ⧬௵44ħ$. We are peacefully and we need your help. I am a scientist/engineer from the planet $⋒◥27⟑▓⍫⋒இǪ$. We calculated that our home star, already an instable red giant, will explode as a supernova in some years.
Our home planet is small, but we have very highly advanced technology at our hands. Our planet is orbiting our home star at an orbit that in its median is a mildly temperate orbit, not too close to be scorching nor too distant to freeze out the planet. Our star is very unstable, as all red giants are, and it may enlarge and shrink chaotically, which would occasionally toast or freeze our planet, but our technology is able to easily cope with that. Exactly, our planet is in a $38.6\text{ }⛮֍㐃$-wide orbit2.
Our problem is that we want that our home planet be able to survive the supernova explosion, but we can't figure out how, so we're sending this signal seeking for your help. We don't want to take refuge elsewhere or just flee, we just want to find a way that allows our planet's surface and atmosphere to survive as much as possible. Having a lump of devastated planetary core and vaporized mantle behind and declaring it as "survived" is not of any use to us.
Further, I am aware of your communication "If the sun were to go supernova, how long would Earth have before it was consumed?" that makes clear that if we don't intervene, nothing of our planet will be left behind. Also, we know about "Can a planet survive a supernova?", but it is not very useful to us, because that was directly to planets which could naturally survive the explosion while we will use our most advanced technologies instead. Also, we know from "If the sun were to go supernova, how long would Earth have before it was consumed?" that if we don't intervene, nothing of our planet will be left behind.
We are also aware of "How can we extinguish a supernova?", but we don't want to either prevent or stop the supernova, but for some... huh... well... RELIGION (yes that is it) reasons that huh... well... our deity asked to us (haha), we now understand that the star needs to reach its natural destiny, but our planet should remain as our lively peace of rock, even if it ends being a very cold one.
So, how could we make our planet survive afterall?
You may think that it is strange that we ask you for that instead of finding the answer ourselves, since we are a very advanced technological civilization. But there is a very simple answer for that. It is easily explainable due to $⍬ईШ3877]֍$
error - signal lost error - data truncated error - data consistency check failed error - syntatic token limit out of bounds fatal - unexpected failure 15894 Please go to http://digital-alien-transceiver.com/bugdatabase/ and file a bug report after checking for duplicates. Don't forget to inform your transceiver configuration parameters. Thank you for your collaboration. info - signal recovered, data reception will be resumed
$Ш568ԖѼ⋒45993⋒ᐉ$ be thick enough, or maybe not completelly, otherwise it won't work. Very simple, isn't it?
I greatly appreciate your help. We are very sure of your peacefully collaboration.
Also, I got this other transmission from my space friend talking to one of his other friends. Looks like some sort of random gossip:
Are you an idiot? I order you to stop right now if you don't want to be executed for insubordination and stupidity. We need to keep our datacenter nearby that freaking3 star when it explodes to collect as much energy possible in order to decrypt the data, not to take it far away.
The only thing that we are still lacking is to find a way to not vaporize our orbiting datacenter-planet before we proccess all the data, and I already told you stop insisting in that moronic idea of "just running away". We're not robotizing an entire planet to just send it to somewhere else, running away like a bunch of $ѦܮḺஹआ$4! That wouldn't make any sense! That won't decrypt the message! So, please, please, keep the focus in your task which as I already told you like $2,985,984$ times is just to preserve the datacenter intact during the explosion until we decrypt that freaking3 message.
Now go back to your actual work, because it is only your department that is behind the schedule, otherwise you will know what is feeling real pain. Even the guys from the stellar Dyson-sphere could figure out how to collect and store the explosion energy, but you on the other hand, seems to be a complete incompetent!
End of secret transmission. Disclosing or leaking the content of this transmission is a crime punishable with a cruel death.
So, that is it: How could we make a planet survive a supernova explosion without it being vaporized or even significantly eroded? There is a very advanced alien civilization working and spending resources on that.
1: A Sol3αling is an inhabitant of some planet called "Sol-3α", i.e. the α-body in the third orbit around some star called "Sol". Could you guess which planet is that?
2: Sorry, I lost my table for converting that distance to Earth-like measurement units, so I don't know exactly how much is $38.6\text{ }⛮֍㐃$. Maybe you could provide the numbers that seems to work best while I search for the table and do the conversion so we don't lose any time?
3: Unsure of the translation of this term. Maybe there is another suitable word starting with the letter "f"?
4: This is some sort of animal-like creature that fears everything and instinctively run away from anything that remotely could pose any danger. A somewhat near translation to English in the sense it was used in the context would be to "running away like a bunch of coward chickens".
BTW, I found out that $2,985,984 = 12^6$. Maybe they count using base 12?
Notes for answerers and dupe-closers:
The aliens may engineer/build anything that they want that do not violate the laws of physics.
In fact they do not need to preserve living beings in the planet. It is just a robotized planet. I.e, a piece of rock that was converted to a giant planet-sized datacenter. Whatever is its atmosphere or surface composition, it is very different than something that would be created by nature. However, whatever is the data-processing hardware that they use in the planet, it must survive the explosion.
Running away, i.e. just moving the planet to somewhere very far from the supernova, do not solves the problem. The aliens need to keep the planet around the supernova. In fact, they are interested in this planet exactly because the star will explode as a supernova.
Note for everybody: I had a lot of answers (21 non-deleted so far), so it was a hard time to nail down the very best.
No answer was perfect. All of them either misses something, contains flaws, are incomplete, overly simplify something, break or abuse the rules, presume some sort of doubtful at best speculative physics, contains some sort of gap or something left vague and unexplained, etc. None of them would give a definitive solid answer if this question had the tag hard-science. Intuition says that it is impossible in hard-science, but being able to prove that there is simply no way ever to manipulate space-time, dark-matter, or whatever else for that (or prove instead that this is indeed possible somehow) is probably way beyond our present-day knowledge level in physics. However, since this question do not have that tag, this is ok.
Anyway, the answers which I consider somewhat acceptable are from Thucydides, John Dallman, Jim2B, Bob Gray, Physicist137, a4android's longer answer and my own non-wiki answer. All of the non-deleted answers posted so far provide some sort of valuable information and insight, even those that are flawed, incomplete or missing the point in some way. Further, almost all of the comments in the question and in most of the answers were very helpful also.
Finally, after a lot of thinking and reasoning with myself, I considered Bob Gray's answer the best (by a tiny margin over the others), so I accepted his answer. Probably, many people will disagree and I am also very unsure myself because I had too many good and very different answers without any of them being perfect or clearly the best.
Finally, I will still evaluate eventual further answers.